The customers will push manufacturers, as there will be demand for both Lightning and Bluetooth. The result will be better and more reliable products, improved tech, more choice, and lower prices. A simple adapter will allow you to use your headphones anywhere you like, and depending on whether there will actually be inductive charging or not (which solves the problem altogether), either your Lightning headphones or a simple adapter will provide a passthrough option, like this:
Not really. All they have to do is buy a $19-29 adapter and they can use any existing analogue headphone currently on the market.